SOLUTION: Hello, I'm having trouble with this problem. Tina made a quilt that was 8 inches taller than it was wide. She then sewed a 4 inch border around the entire quilt. If the area of th

Question 913079: Hello, I'm having trouble with this problem.
Tina made a quilt that was 8 inches taller than it was wide. She then sewed a 4 inch border around the entire quilt. If the area of the quilt and its border is 1920 square inches, find the dimensions of the quilt without the border?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Tina made a quilt that was 8 inches taller than it was wide.
She then sewed a 4 inch border around the entire quilt.
If the area of the quilt and its border is 1920 square inches, find the dimensions of the quilt without the border?
:
Let w = the width of the original quilt
then
(w+8) = the length of the original quilt
:
Sewing a 4" border around the quilt will add 8" to each dimension
therefore
(w+8) * (w+8+8) = 1920
(w+8) * (w+16) = 1920
FOIL
w^2 + 16w + 8w + 128 = 1920
w^2 + 24w + 128 - 1920 = 0
A quadratic equation
w^2 + 24w - 1792 = 0
you can use the quadratic formula, but this will factor to:
(w-32)(w+56) = 0
The positive solution is all we want here
w = 32" is width of the original quilt
then
32 + 8 = 40" is length
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